Halo nuclei in a three-body model and universal characteristics of low-energy few-body systems

Within general characteristics of low-energy few-body systems, we revise some well-known correlations found in nuclear physics, and the properties of low-mass halo nuclei in a three-body neutron-neutron-core model. In this context, near the critical conditions for the occurrence of an Efimov state, we report some results obtained for the neutron- 19C elastic scattering. © 2010 American Institute of Physics.

Scales and Universality in Few-Body Systems

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Messung des Realteils der gebundenen 3 He-Streulänge

Streulängen beschreiben die s-Wellen-Streuung niederenergetischer Neutronen an Kernen. Solche Streuprozesse laufen nahezu ausschließlich über die starke Wechselwirkung ab. Wegen der Spinabhängigkeit der starken Wechselwirkung werden den Multiplett-Streulängen, d.h. den Streulängen der Gesamtspinzustände J, im Allgemeinen verschiedene Werte zugeordnet. Im Experiment sind die Multiplett-Streuzustände an makroskopischen Proben in der Regel nicht unmittelbar zugänglich. Messbar sind jedoch der polarisationsabhängige und -unabhängige Anteil der Streulänge, welche als inkohärente Streulänge und kohärente Streulänge bezeichnet werden und Linearkombinationen der Multiplettstreulängen sind. Durch komplexe Streulängen lässt sich der für reine Streuprozesse entwickelte Formalismus erweitern: Der Imaginärteil der Streulänge beschreibt dann die Absorption von Projektilen im Target. Sämtliche Reaktionsquerschnitte lassen sich als Funktionen der Streulänge angeben. Verbesserte Messungen der 3He-Streulängen sind für die Entwicklung theoretischer Modelle von Wenig-Nukleonen-Systemen wichtig. Für die Systeme (n,D) und (n,T) wurden in den letzten Jahren u.a. präzise theoretische Vorhersagen für die Multiplett-Streulängen gemacht. Die Übereinstimmung mit den experimentellen Ergebnissen untermauert, dass die theoretischen Unsicherheiten dieser Werte nur etwa 1 Promille betragen. Demgegenüber ist die theoretische Behandlung des n-3He-Systems aufwändiger. Bis zu Beginn der 1980er Jahre wurde eine Reihe von Vorhersagen für die Multiplett-Streulängen gemacht, die auf erfolgreichen Dreinukleon-Potentialmodellen basierten, untereinander aber vollkommen inkompatibel waren. Daneben waren zwei disjunkte Wertepaare für die Multiplett-Streulängen mit den experimentellen Ergebnissen verträglich. Obwohl es begründete Argumente zugunsten eines der Wertepaare gab, bestand die Hoffnung auf eine experimentelle Verifikation durch direkte Messung der inkohärenten Streulänge bereits 1980. Die Bestimmung des Realteils der inkohärenten Streulänge liefert in der Multiplettstreulängenebene eine Gerade, die fast orthogonal zum Band des Realteils der kohärenten Streulänge verläuft. Vermutlich aufgrund der unzureichenden Kenntnis der Realteile hat in den letzten Jahren keine nennenswerte Weiterentwicklung der Modelle für das System n–3He stattgefunden. Diese Arbeit entstand in der Absicht, durch polarisierte und unpolarisierte Experimente an 3He quantitative Fakten zur Beurteilung konkurrierender Vier-Nukleonen-Modelle zu schaffen und somit der theoretischen Arbeit auf diesem Feld einen neuen Impuls zu geben. Eine jüngst veröffentlichte theoretische Arbeit [H. M. Hofmann und G. M. Hale. Phys. Rev. C, 68(021002(R)): 1–4, Apr. 2003] zur spinabhängigen Streulänge des 3He belegt, dass die im Rahmen dieser Arbeit unternommenen Anstrengungen auf reges Interesse stoßen. Durch die Anwendung zweier sehr unterschiedlicher experimenteller Konzepte wurden Präzisionsmessungen der Realteile der kohärenten und inkohärenten Neutronenstreulänge des 3He durchgeführt. Während sich die Methode der Neutroneninterferometrie seit Ende der 1970er Jahre als Standardverfahren zur Messung von spinunabhängigen Streulängen etabliert hat, handelt es sich bei der Messung des pseudomagnetischen Präzessionswinkels am Spinecho-Spektrometer um ein neues experimentelles Verfahren. Wir erhalten aus den Experimenten für die gebundenen kohärenten und inkohärenten Streulängen neue Werte, welche die Unsicherheiten im Falle der kohärenten Streulänge um eine Größenordnung, im Falle der inkohärenten Streulänge sogar um den Faktor 30 reduzieren. Die Kombination dieser Resultate liefert verbesserte Werte der, für die nukleare Wenigkörper-Theorie wichtigen, Singulett- und Triplett-Streulängen. Wir erhalten neue Werte für die kohärenten und inkohärenten Anteile des gebundenen Streuquerschnitts, das für die Neutronenstreuung an der 3He-Quantenflüssigkeit wichtige Verhältnis von inkohärentem und kohärentem Streuquerschnitt und für den freien totalen Streuquerschnitt.

LARGE ATOMIC and NUCLEAR THREE-BODY SYSTEMS: SCATTERING and BINDING

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Scales, Universality and Finite-Range Correction in Three-body Systems

The scale invariance manifested by the weakly-bound Efimov states implies that all the Efimov spectrum can be merged in a single scaling function. By considering this scaling function, the ratio between two consecutive energy levels, E3 (N+1) and E3 (N), can be obtained from a two-body low-energy observable (usually the scattering length a), given in units of the three-body energy level N. The zero-ranged scaling function is improved by incorporating finite range corrections in first order of r0/a (r0 is the potential effective range). The critical condition for three-identical bosons in s-wave, when the excited E3 (N+1) state disappears in the 2 + 1 threshold, is given by √E2/E3 (N) ≈ 0.38+0.12(r0/a). © 2012 Springer-Verlag.

Structure of exotic three-body systems

The classification of large halos formed by two identical particles and a core is systematically addressed according to interparticle distances. The root-mean-square distances between the constituents are described by universal scaling functions obtained from a renormalized zero-range model. Applications for halo nuclei, Li-11 and Be-14, and for atomicn He-4(3) are briefly discussed. The generalization to four-body systems is proposed.

Tjon Lines and Scaling Limit in Four-Body Systems

The fixed-slope correlation between tetramer and trimer binding energies, observed by Tjon in the context of nuclear physics, is mainly a manifestation of the dominance of the two-nucleon force in the nuclear potential, which makes the four-body scale on the order of the three-body one. In a more general four-boson case, the correlation between tetramer and trimer binding energies has a non-fixed slope, which expresses the dependence on the new scale. The associated scaling function generates a family of Tjon lines. This conclusion relies on a recent study with weakly-bound four identical bosons, within a renormalized zero-range Faddeev-Yakubovsky formalism. © 2012 Springer-Verlag.

Mass-Imbalanced Three-Body Systems in 2D: Bound States and the Analytical Approach to the Adiabatic Potential

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Universality of Three-Body Systems in 2D: Parametrization of the Bound States Energies

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Inelastic neutron scattering in spectroscopic studies of hydrogen on carbon-supported catalysts-experimental spectra and computed spectra of model systems

Inelastic neutron scattering spectroscopy has been used to observe and characterise hydrogen on the carbon component of a Pt/C catalyst. INS provides the complete vibration spectrum of coronene, regarded as a molecular model of a graphite layer. The vibrational modes are assigned with the aid of ab initio density functional theory calculations and the INS spectra by the a-CLIMAX program. A spectrum for which the H modes of coronene have been computationally suppressed, a carbon-only coronene spectrum, is a better representation of the spectrum of a graphite layer than is coronene itself. Dihydrogen dosing of a Pt/C catalyst caused amplification of the surface modes of carbon, an effect described as H riding on carbon. From the enhancement of the low energy carbon modes (100-600 cm(-1)) it is concluded that spillover hydrogen becomes attached to dangling bonds at the edges of graphitic regions of the carbon support. (C) 2003 Elsevier Science B.V. All rights reserved.

Multiple-scattering in radar systems: a review

Although extensively studied within the lidar community, the multiple scattering phenomenon has always been considered a rare curiosity by radar meteorologists. Up to few years ago its appearance has only been associated with two- or three-body-scattering features (e.g. hail flares and mirror images) involving highly reflective surfaces. Recent atmospheric research aimed at better understanding of the water cycle and the role played by clouds and precipitation in affecting the Earth's climate has driven the deployment of high frequency radars in space. Examples are the TRMM 13.5 GHz, the CloudSat 94 GHz, the upcoming EarthCARE 94 GHz, and the GPM dual 13-35 GHz radars. These systems are able to detect the vertical distribution of hydrometeors and thus provide crucial feedbacks for radiation and climate studies. The shift towards higher frequencies increases the sensitivity to hydrometeors, improves the spatial resolution and reduces the size and weight of the radar systems. On the other hand, higher frequency radars are affected by stronger extinction, especially in the presence of large precipitating particles (e.g. raindrops or hail particles), which may eventually drive the signal below the minimum detection threshold. In such circumstances the interpretation of the radar equation via the single scattering approximation may be problematic. Errors will be large when the radiation emitted from the radar after interacting more than once with the medium still contributes substantially to the received power. This is the case if the transport mean-free-path becomes comparable with the instrument footprint (determined by the antenna beam-width and the platform altitude). This situation resembles to what has already been experienced in lidar observations, but with a predominance of wide- versus small-angle scattering events. At millimeter wavelengths, hydrometeors diffuse radiation rather isotropically compared to the visible or near infrared region where scattering is predominantly in the forward direction. A complete understanding of radiation transport modeling and data analysis methods under wide-angle multiple scattering conditions is mandatory for a correct interpretation of echoes observed by space-borne millimeter radars. This paper reviews the status of research in this field. Different numerical techniques currently implemented to account for higher order scattering are reviewed and their weaknesses and strengths highlighted. Examples of simulated radar backscattering profiles are provided with particular emphasis given to situations in which the multiple scattering contributions become comparable or overwhelm the single scattering signal. We show evidences of multiple scattering effects from air-borne and from CloudSat observations, i.e. unique signatures which cannot be explained by single scattering theory. Ideas how to identify and tackle the multiple scattering effects are discussed. Finally perspectives and suggestions for future work are outlined. This work represents a reference-guide for studies focused at modeling the radiation transport and at interpreting data from high frequency space-borne radar systems that probe highly opaque scattering media such as thick ice clouds or precipitating clouds.

Extracting quantitative structural parameters for disordered polymers from neutron scattering data

The organization of non-crystalline polymeric materials at a local level, namely on a spatial scale between a few and 100 a, is still unclear in many respects. The determination of the local structure in terms of the configuration and conformation of the polymer chain and of the packing characteristics of the chain in the bulk material represents a challenging problem. Data from wide-angle diffraction experiments are very difficult to interpret due to the very large amount of information that they carry, that is the large number of correlations present in the diffraction patterns.We describe new approaches that permit a detailed analysis of the complex neutron diffraction patterns characterizing polymer melts and glasses. The coupling of different computer modelling strategies with neutron scattering data over a wide Q range allows the extraction of detailed quantitative information on the structural arrangements of the materials of interest. Proceeding from modelling routes as diverse as force field calculations, single-chain modelling and reverse Monte Carlo, we show the successes and pitfalls of each approach in describing model systems, which illustrate the need to attack the data analysis problem simultaneously from several fronts.

Scales of critically stable few-body halo systems

We review the scaling properties of few-body observables near the critical conditions for binding, with particular attention to light exotic nuclei, molecules and ultracold atoms.

Effective theory for trapped few-fermion systems

We apply the general principles of effective field theories to the construction of effective interactions suitable for few- and many-body calculations in a no-core shell model framework. We calculate the spectrum of systems with three and four two-component fermions in a harmonic trap. In the unitary limit, we find that three-particle results are within 10% of known semianalytical values even in small model spaces. The method is very general, and can be readily extended to other regimes, more particles, different species (e.g., protons and neutrons in nuclear physics), or more-component fermions (as well as bosons). As an illustration, we present calculations of the lowest-energy three-fermion states away from the unitary limit and find a possible inversion of parity in the ground state in the limit of trap size large compared to the scattering length. Furthermore, we investigate the lowest positive-parity states for four fermions, although we are limited by the dimensions we can currently handle in this case.